Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def check_number( arr, no ) :
    i = 0
    j = len( arr ) - 1 
    while i <= j :
        if arr[i] + arr[j] == no :
            return "YES"
        elif arr[i] + arr[j] > no :
            j -= 1
        else :
            i += 1
    return "NO"

def check_funky( n ) :
    i = 1
    arr = []
    while i * ( i + 1 ) // 2 <= 10 ** 9 :
        arr.append(i * ( i + 1 ) // 2)
        i += 1
    return  check_number( arr, n )

if __name__ == "__main__" :
    n = int(input())
    print(check_funky( n ))